Currently, the wireless personal area network (WPAN), which operates within the millimeter-wave spectrum around 60 GHz and has transmission speed of several Gbps, is lively discussed in the IEEE 802.15.3c standardization task group. The current standardization specification defines four WPC codes, LDPC(1440,1340), LDPC(672,588), LDPC(672,504), and LDPC(672,336) for channel coding. The sum-product decoding method is generally used to decode the LDPC codes. In this decoding method, it is necessary to give the following log-likelihood ratio of the channel output of the n-th transmission bit as input:
                              λ          n                =                  log          ⁢                                    P              ⁡                              (                                                                            y                      n                                        ❘                                          x                      n                                                        =                  1                                )                                                    P              ⁡                              (                                                                            y                      n                                        ❘                                          x                      n                                                        =                                      -                    1                                                  )                                                                        [                  Eq          .                                          ⁢          1                ]            where xn is the n-th transmission bit and yn is the corresponding output information bit from the channel.
For example, if the binary phase shift keying (BPSK) is used as a modulation scheme and the additive white Gaussian noise (AWGN: variance=the square of σ) is assumed as noise, the input log-likelihood ratio is given as follows:
                              λ          n                =                              2            ⁢                          y              n                                            σ            2                                              [                  Eq          .                                          ⁢          2                ]            where, if the SN ratio of the communication channel is SNR[dB], the AWGN variance or the square of σ is given by:σ2=10−SNR/10  [Eq. 3]
Moreover, if the communication channel is a binary symmetric channel, the following relation is satisfied:
                              λ          n                =                  {                                                                                          log                    ⁢                                          p                                              1                        -                        p                                                                              ;                                                                                                  y                    n                                    =                                      -                    1                                                                                                                                            log                    ⁢                                                                  1                        -                        p                                            p                                                        ;                                                                                                  y                    n                                    =                  1                                                                                        [                  Eq          .                                          ⁢          4                ]            where an error probability p is given by:p=0.5erfc(√{square root over (1/σ2)})  [Eq. 5]
As apparent from these equations, the noise variance decreases as the SN ratio of the communication channel increases. As a result, both the average value of the input log-likelihood ratio and the variance increase.
When applying the LDPC codes to an application, which requests a high throughput, such as an uncompressed HDTV video transfer using millimeter-wave transmission system, it is common to implement a decoder by a fixed-point arithmetic operation. In this case, the range of numeric values which the decoder can handle dynamic range) is limited to a finite range. Therefore, if the input log-likelihood ratio is high, an error floor occurs due to an overflow or an underflow, thereby significantly degrading the performance of the decoder.
To prevent the overflow or underflow, it is necessary to prepare a large dynamic range, though it increases the circuit size. Moreover, an actual receiver needs to process received signals by using an AD converter and to input the received signals to a decoder. If high-speed processing is required, a full flash type AD converter is used. The full flash type AD converter provides high-speed AD conversion by arranging a lot of comparators for the input signals and comparing all bits at a time. To obtain output digital signals having a dynamic range of N bits, however, O (2 to N-th power) comparators are needed. Therefore, an increase in the circuit size is inevitable to treat input signals having large values.
U.S. Pat. No. 7,231,577, hereinafter referred to as “Patent Document 1,” is entitled “soft information scaling for iterative decoding.”
X.-Y. Hu, E. Eleftheriou, D-M Arnold, and A. Dholakia, “Efficient Implementations of the Sum-Product Algorithm for Decoding LDPC Codes,” GLOBECOM 2001, is hereinafter referred to as “Non-patent Document 1,” and is completely incorporated herein by reference in its entirety for all purposes.